Assume that$$ women's heights are normally distributed with a mean given by $63\mathrm{.}7$ in$,$ and a standard deviation given by $2\mathrm{.}2$in $.$ Complete parts a and b$.$

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Part $1$

a$.$ If $1$ woman is randomly$$ selected, find the probability that her height is between in $62\mathrm{.}8$ and $63\mathrm{.}8$ in$.$

The probability is approximately